Question

A figure is a regular n-gon. Which of the following

Answer 1

Answer:

The correct answer is D. 360°

Step-by-step explanation:

The sum of all the exterior angles of a regular n-gon or a polygon is always equal to 360°.

Let us consider the image attached.

First of all let us consider the triangle.

As per the property of exterior angles: The exterior angle is equal to the sum of 2 opposite interior angles.

$\Rightarrow \angle 1=\angle B + \angle C\\\Rightarrow \angle 2=\angle A + \angle C\\\Rightarrow \angle 3=\angle A + \angle B$

Where $\angle A, \angle B\ and\ \angle C$ are the interior angles of the triangle.

Adding the above equations:

$\angle 1 +\angle 2 +\angle 3 = 2 \times (\angle A +\angle B +\angle C )$

The sum of interior angles of a triangle is always equal to 180°

$\angle A +\angle B +\angle C = 180^\circ$

$\angle 1 +\angle 2 +\angle 3 = 2 \times 180^\circ\\\Rightarrow \angle 1 +\angle 2 +\angle 3 = 360^\circ$

Hence, proved that the sum of exterior angles is $360^\circ$.

So, the correct answer is D. $360^\circ$